SME
Grade 6 Math · Problem type
Ratios with three parts
Use this for “A ratio of 3:4:5 with 96 people in all. How many in each part?”
Diagram
3 : 4 : 5 makes 12 equal parts, each worth 8.
Total: 96.
This is an example. Type your own values to start a new problem.
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Parts in all
worked out (not typed)
One part is worth
worked out (not typed)
Formulas
24 + 32 + 40 = 96
First amount + second amount + third amount = total
3 + 4 + 5 = 12
First part + second part + third part = parts in all
96 ÷ 12 = 8
Total ÷ parts in all = one part is worth
3 × 8 = 24
First part × one part is worth = first amount
4 × 8 = 32
Second part × one part is worth = second amount
5 × 8 = 40
Third part × one part is worth = third amount
Assumptions
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Every box in the three tapes is worth the same amount.
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Share the total among all the boxes, then multiply for each part.
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Parts of the ratio are whole numbers to 12.
Step-by-step
WE KNOW
First part of the ratio: 3
Second part of the ratio: 4
Third part of the ratio: 5
Total: 96
FIND
parts in all, one part is worth, first amount, second amount, third amount
Step 1 · Find parts in all
3 + 4 + 5 = ?
First part + second part + third part = parts in all
Count the boxes in all three tapes.
Parts in all = 12
Step 2 · Find one part is worth
96 ÷ 12 = ?
Total ÷ parts in all = one part is worth
Share the total equally among all the boxes.
One part is worth = 8
Step 3 · Find first amount
3 × 8 = ?
First part × one part is worth = first amount
Multiply that tape’s boxes by what one box is worth.
First amount = 24
Step 4 · Find second amount
4 × 8 = ?
Second part × one part is worth = second amount
Multiply that tape’s boxes by what one box is worth.
Second amount = 32
Step 5 · Find third amount
5 × 8 = ?
Third part × one part is worth = third amount
Multiply that tape’s boxes by what one box is worth.
Third amount = 40
Check
Put the numbers back in. Both sides should match.
24 + 32 + 40 = 96 ✓
3 + 4 + 5 = 12 ✓
8 × 12 = 96 ✓
3 × 8 = 24 ✓
4 × 8 = 32 ✓
5 × 8 = 40 ✓
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Related lessons
Understand and use ratios
Main lesson
Solve ratio problems with tape diagrams
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Ratio language
Use this for “For every 2 cats there are 3 dogs”: the ratio of cats to dogs.
Equivalent ratios
Use this for “Is 4:6 equivalent to 2:3?”